Although not strictly an answer to your question, the term "half birthday" is common in the USA. It means six months after your birthday. Its usage is common in grade school, so that classes can celebrate the birthdays of children whose birthday falls during the summer vacation.
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Fraser OrrDec 30 '11 at 1:56

There had been some attempts in trying to promote the use of certain neologisms, but none of them apparently really caught on. The safest way of referring to such dates is by using the simpler term anniversary preceded by the period.

I wouldn't personally use any other alternative. Imagine that if they can't agree on a basic period like a month, what is left for fortnights or weeks or any other less common arbitrary period of time.

I use "six-month anniversary" and similar terms. Strictly speaking, you're not supposed to do that because "anniversary" comes from the Latin "annus" which means "year", but communication is achieved nevertheless. Nobody has ever asked me to clarify the term "two-month anniversary" for example.
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IreneDec 28 '11 at 8:12

@tchrist You are right. However I think it's worth mentioning that catched used to be the simple past of to catch up to some time where its use started to decline in favor of caught. Nonetheless, the past tense of the phrasal to catch on was never catched on but caught on; so ... +1 and my apologies. Wiktionary: catched (obsolete or nonstandard) Simple past tense and past participle of catch. Synonyms: caught
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EduardoDec 29 '11 at 3:35